Question

We are interested in soda consumption among UW-Madison students. We have data from a sample of 29 Soc 360 students. For these purposes we will consider our sample a SRS from the population of interest. Assume that 29 is a large enough n so that the sampling distribution will be Normal. Further suppose we know that the standard deviation of the number of bottles/cans of soda consumed in a day among UW-Madison students is 0.72. The mean number of bottle/cans of soda consumed by our sample members in a day is 0.39. (a) We would like to know whether there is evidence that the average UW-Madison student consumes less than ½ a bottle/can of soda per day. State the null and alternative hypotheses in formal notation. (b) What is the population parameter we are interested in making inference about (in words)? (c) Draw a picture of the sampling distribution for this test. Label the population and sample means. Shade the area that gives the p-value of interest. (d) Find the test statistic (z). Add the test statistic to the picture of your sampling distribution. (e) Report and interpret the p-value. (Follow one of the examples from the lecture in writing your interpretation of the p-value.) (f) Are your results significant at the 5% level? Interpret your results referring to both the null and the alternative hypotheses (Follow one of the examples from lecture in writing your interpretation).

Answer 1

a)

Ho: μ=0.5

Ha: μ<0.5

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population parameter is-soda consumption among UW-Madison student

We would like to know whether there is evidence that the average UW-Madison student consumes less than ½ a bottle/can of soda per day

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The p-value is p = 0.2053.

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since p=0.2053≥0.05,result is not significant

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Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that average UW-Madison student consumes less than ½ a bottle/can of soda per day.